Separability of analytic postnonlinear blind source separation with bounded sources

The aim of blind source separation (BSS) is to transform a mixed random vector such that the original sources are recovered. If the sources are assumed to be statistically independent, independent component analysis (ICA) can be applied to perform BSS. An important aspect of successfully analysing data with BSS is to know the indeterminacies of the problem, that is how the separating model is related to the original mixing model. In the case of linear ICA-based BSS it is well known that the mixing matrix can be found except for permutation and scaling, but for more general settings not many results exist. In this work we only consider random variables with bounded densities. We will shortly describe the bounded BSS problem for linear mixtures. Then, we generalize these ideas to the postnonlinear mixing model with analytic nonlinearities and calculate its indeterminacies